Answer:
import math
#Initialize tolerance
tolerance = 0.000001
def newton(x):
    """ Returns the square root of x """
    #Performs the successive approximations
    estimate = 1.0
    while True:
        estimate = (estimate + x / estimate) / 2
        difference = abs(x - estimate ** 2)
        if difference <= tolerance:     # Break out of loop if difference is less than tolerance
            break            
        return estimate     # While the difference value is > TOLERANCE, the process continues
def main():
    """Allows the user to obtain square roots."""
    while True:
        #Receive the input number from the user
        x = input("Enter a positive number or enter/return to quit: ")
        if x == "":     #if user presses "Enter" then exit the program
            break       # Otherwise, continue the process of allowing new numbers
        x = float(x)
        #Output the result
        print("The programs estimate of the square root of ", x, "is ", round(newton(x),2))
        print("Python's estimate: ", math.sqrt(x))
main()